Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(19,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.n (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.19 |
Dual form | 756.2.n.a.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 1.36603i | 0.258819 | − | 0.965926i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | ||||
\(5\) | 3.46410i | 1.54919i | 0.632456 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | − | 2.00000i | −0.654654 | − | 0.755929i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.73205 | + | 1.26795i | 1.49641 | + | 0.400961i | ||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.50000 | − | 2.59808i | 1.24808 | − | 0.720577i | 0.277350 | − | 0.960769i | \(-0.410544\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | −3.36603 | + | 1.63397i | −0.899608 | + | 0.436698i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 4.50000 | − | 2.59808i | 1.09141 | − | 0.630126i | 0.157459 | − | 0.987526i | \(-0.449670\pi\) |
0.933952 | + | 0.357400i | \(0.116337\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.866025 | − | 1.50000i | 0.198680 | − | 0.344124i | −0.749421 | − | 0.662094i | \(-0.769668\pi\) |
0.948101 | + | 0.317970i | \(0.103001\pi\) | |||||||
\(20\) | 3.46410 | − | 6.00000i | 0.774597 | − | 1.34164i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.73205 | − | 0.732051i | −0.582475 | − | 0.156074i | ||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | −1.90192 | − | 7.09808i | −0.372998 | − | 1.39205i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | + | 5.19615i | 0.188982 | + | 0.981981i | ||||
\(29\) | 2.50000 | − | 4.33013i | 0.464238 | − | 0.804084i | −0.534928 | − | 0.844897i | \(-0.679661\pi\) |
0.999167 | + | 0.0408130i | \(0.0129948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.59808 | − | 4.50000i | 0.466628 | − | 0.808224i | −0.532645 | − | 0.846339i | \(-0.678802\pi\) |
0.999273 | + | 0.0381148i | \(0.0121353\pi\) | |||||||
\(32\) | 5.46410 | − | 1.46410i | 0.965926 | − | 0.258819i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.90192 | − | 7.09808i | −0.326177 | − | 1.21731i | ||||
\(35\) | 6.92820 | − | 6.00000i | 1.17108 | − | 1.01419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | + | 2.59808i | −0.246598 | + | 0.427121i | −0.962580 | − | 0.270998i | \(-0.912646\pi\) |
0.715981 | + | 0.698119i | \(0.245980\pi\) | |||||||
\(38\) | −1.73205 | − | 1.73205i | −0.280976 | − | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.92820 | − | 6.92820i | −1.09545 | − | 1.09545i | ||||
\(41\) | −1.50000 | + | 0.866025i | −0.234261 | + | 0.135250i | −0.612536 | − | 0.790443i | \(-0.709851\pi\) |
0.378275 | + | 0.925693i | \(0.376517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.52628 | + | 5.50000i | 1.45274 | + | 0.838742i | 0.998636 | − | 0.0522047i | \(-0.0166248\pi\) |
0.454108 | + | 0.890947i | \(0.349958\pi\) | |||||||
\(44\) | −2.00000 | + | 3.46410i | −0.301511 | + | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.46410 | − | 1.46410i | −0.805638 | − | 0.215870i | ||||
\(47\) | −0.866025 | − | 1.50000i | −0.126323 | − | 0.218797i | 0.795926 | − | 0.605393i | \(-0.206984\pi\) |
−0.922249 | + | 0.386596i | \(0.873651\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | −2.56218 | + | 9.56218i | −0.362347 | + | 1.35230i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.3923 | −1.44115 | ||||||||
\(53\) | 0.500000 | + | 0.866025i | 0.0686803 | + | 0.118958i | 0.898321 | − | 0.439340i | \(-0.144788\pi\) |
−0.829640 | + | 0.558298i | \(0.811454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.92820 | 0.934199 | ||||||||
\(56\) | 7.46410 | + | 0.535898i | 0.997433 | + | 0.0716124i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.00000 | − | 5.00000i | −0.656532 | − | 0.656532i | ||||
\(59\) | 0.866025 | − | 1.50000i | 0.112747 | − | 0.195283i | −0.804130 | − | 0.594454i | \(-0.797368\pi\) |
0.916877 | + | 0.399170i | \(0.130702\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.50000 | − | 2.59808i | 0.576166 | − | 0.332650i | −0.183442 | − | 0.983030i | \(-0.558724\pi\) |
0.759608 | + | 0.650381i | \(0.225391\pi\) | |||||||
\(62\) | −5.19615 | − | 5.19615i | −0.659912 | − | 0.659912i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 9.00000 | + | 15.5885i | 1.11631 | + | 1.93351i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.79423 | − | 4.50000i | −0.952217 | − | 0.549762i | −0.0584478 | − | 0.998290i | \(-0.518615\pi\) |
−0.893769 | + | 0.448528i | \(0.851948\pi\) | |||||||
\(68\) | −10.3923 | −1.26025 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.66025 | − | 11.6603i | −0.676530 | − | 1.39367i | ||||
\(71\) | 2.00000i | 0.237356i | 0.992933 | + | 0.118678i | \(0.0378657\pi\) | ||||
−0.992933 | + | 0.118678i | \(0.962134\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5000 | + | 6.06218i | −1.22893 | + | 0.709524i | −0.966807 | − | 0.255510i | \(-0.917757\pi\) |
−0.262126 | + | 0.965034i | \(0.584423\pi\) | |||||||
\(74\) | 3.00000 | + | 3.00000i | 0.348743 | + | 0.348743i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.00000 | + | 1.73205i | −0.344124 | + | 0.198680i | ||||
\(77\) | −4.00000 | + | 3.46410i | −0.455842 | + | 0.394771i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.59808 | + | 1.50000i | −0.292306 | + | 0.168763i | −0.638982 | − | 0.769222i | \(-0.720644\pi\) |
0.346675 | + | 0.937985i | \(0.387311\pi\) | |||||||
\(80\) | −12.0000 | + | 6.92820i | −1.34164 | + | 0.774597i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.633975 | + | 2.36603i | 0.0700108 | + | 0.261284i | ||||
\(83\) | −2.59808 | + | 4.50000i | −0.285176 | + | 0.493939i | −0.972652 | − | 0.232268i | \(-0.925385\pi\) |
0.687476 | + | 0.726207i | \(0.258719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | + | 15.5885i | 0.976187 | + | 1.69081i | ||||
\(86\) | 11.0000 | − | 11.0000i | 1.18616 | − | 1.18616i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.00000 | + | 4.00000i | 0.426401 | + | 0.426401i | ||||
\(89\) | −7.50000 | − | 4.33013i | −0.794998 | − | 0.458993i | 0.0467209 | − | 0.998908i | \(-0.485123\pi\) |
−0.841719 | + | 0.539915i | \(0.818456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.9904 | − | 4.50000i | −1.36176 | − | 0.471728i | ||||
\(92\) | −4.00000 | + | 6.92820i | −0.417029 | + | 0.722315i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.36603 | + | 0.633975i | −0.244037 | + | 0.0653895i | ||||
\(95\) | 5.19615 | + | 3.00000i | 0.533114 | + | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.50000 | + | 0.866025i | 0.152302 | + | 0.0879316i | 0.574214 | − | 0.818705i | \(-0.305308\pi\) |
−0.421912 | + | 0.906637i | \(0.638641\pi\) | |||||||
\(98\) | 9.09808 | + | 3.90192i | 0.919044 | + | 0.394154i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.1244 | + | 7.00000i | 1.21244 | + | 0.700000i | ||||
\(101\) | − | 17.3205i | − | 1.72345i | −0.507371 | − | 0.861727i | \(-0.669383\pi\) | ||
0.507371 | − | 0.861727i | \(-0.330617\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −3.80385 | + | 14.1962i | −0.372998 | + | 1.39205i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.36603 | − | 0.366025i | 0.132680 | − | 0.0355515i | ||||
\(107\) | −6.06218 | − | 3.50000i | −0.586053 | − | 0.338358i | 0.177482 | − | 0.984124i | \(-0.443205\pi\) |
−0.763535 | + | 0.645766i | \(0.776538\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.50000 | − | 2.59808i | −0.143674 | − | 0.248851i | 0.785203 | − | 0.619238i | \(-0.212558\pi\) |
−0.928877 | + | 0.370387i | \(0.879225\pi\) | |||||||
\(110\) | 2.53590 | − | 9.46410i | 0.241788 | − | 0.902367i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.46410 | − | 10.0000i | 0.327327 | − | 0.944911i | ||||
\(113\) | 9.50000 | + | 16.4545i | 0.893685 | + | 1.54791i | 0.835424 | + | 0.549606i | \(0.185222\pi\) |
0.0582609 | + | 0.998301i | \(0.481444\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.8564 | 1.29212 | ||||||||
\(116\) | −8.66025 | + | 5.00000i | −0.804084 | + | 0.464238i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.73205 | − | 1.73205i | −0.159448 | − | 0.159448i | ||||
\(119\) | −12.9904 | − | 4.50000i | −1.19083 | − | 0.412514i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −1.90192 | − | 7.09808i | −0.172192 | − | 0.642630i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.00000 | + | 5.19615i | −0.808224 | + | 0.466628i | ||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.00000i | − | 0.532414i | −0.963916 | − | 0.266207i | \(-0.914230\pi\) | ||
0.963916 | − | 0.266207i | \(-0.0857705\pi\) | |||||||
\(128\) | −10.9282 | − | 2.92820i | −0.965926 | − | 0.258819i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 24.5885 | − | 6.58846i | 2.15655 | − | 0.577846i | ||||
\(131\) | 13.8564 | 1.21064 | 0.605320 | − | 0.795982i | \(-0.293045\pi\) | ||||
0.605320 | + | 0.795982i | \(0.293045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.50000 | + | 0.866025i | −0.390199 | + | 0.0750939i | ||||
\(134\) | −9.00000 | + | 9.00000i | −0.777482 | + | 0.777482i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.80385 | + | 14.1962i | −0.326177 | + | 1.21731i | ||||
\(137\) | −8.00000 | −0.683486 | −0.341743 | − | 0.939793i | \(-0.611017\pi\) | ||||
−0.341743 | + | 0.939793i | \(0.611017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2583 | + | 19.5000i | 0.954919 | + | 1.65397i | 0.734553 | + | 0.678551i | \(0.237392\pi\) |
0.220366 | + | 0.975417i | \(0.429275\pi\) | |||||||
\(140\) | −18.0000 | + | 3.46410i | −1.52128 | + | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.73205 | + | 0.732051i | 0.229269 | + | 0.0614323i | ||||
\(143\) | −5.19615 | − | 9.00000i | −0.434524 | − | 0.752618i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.0000 | + | 8.66025i | 1.24568 | + | 0.719195i | ||||
\(146\) | 4.43782 | + | 16.5622i | 0.367277 | + | 1.37070i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.19615 | − | 3.00000i | 0.427121 | − | 0.246598i | ||||
\(149\) | 4.00000 | 0.327693 | 0.163846 | − | 0.986486i | \(-0.447610\pi\) | ||||
0.163846 | + | 0.986486i | \(0.447610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0000i | 1.13930i | 0.821886 | + | 0.569652i | \(0.192922\pi\) | ||||
−0.821886 | + | 0.569652i | \(0.807078\pi\) | |||||||
\(152\) | 1.26795 | + | 4.73205i | 0.102844 | + | 0.383820i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.26795 | + | 6.73205i | 0.263339 | + | 0.542484i | ||||
\(155\) | 15.5885 | + | 9.00000i | 1.25210 | + | 0.722897i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.5000 | − | 6.06218i | −0.837991 | − | 0.483814i | 0.0185897 | − | 0.999827i | \(-0.494082\pi\) |
−0.856581 | + | 0.516013i | \(0.827416\pi\) | |||||||
\(158\) | 1.09808 | + | 4.09808i | 0.0873583 | + | 0.326025i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.07180 | + | 18.9282i | 0.400961 | + | 1.49641i | ||||
\(161\) | −8.00000 | + | 6.92820i | −0.630488 | + | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.79423 | − | 4.50000i | −0.610491 | − | 0.352467i | 0.162667 | − | 0.986681i | \(-0.447991\pi\) |
−0.773158 | + | 0.634214i | \(0.781324\pi\) | |||||||
\(164\) | 3.46410 | 0.270501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.19615 | + | 5.19615i | 0.403300 | + | 0.403300i | ||||
\(167\) | −2.59808 | − | 4.50000i | −0.201045 | − | 0.348220i | 0.747820 | − | 0.663901i | \(-0.231100\pi\) |
−0.948865 | + | 0.315681i | \(0.897767\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | − | 12.1244i | 0.538462 | − | 0.932643i | ||||
\(170\) | 24.5885 | − | 6.58846i | 1.88585 | − | 0.505312i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.0000 | − | 19.0526i | −0.838742 | − | 1.45274i | ||||
\(173\) | 16.5000 | − | 9.52628i | 1.25447 | − | 0.724270i | 0.282477 | − | 0.959274i | \(-0.408844\pi\) |
0.971994 | + | 0.235004i | \(0.0755104\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.1244 | + | 14.0000i | 0.916515 | + | 1.05830i | ||||
\(176\) | 6.92820 | − | 4.00000i | 0.522233 | − | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.66025 | + | 8.66025i | −0.649113 | + | 0.649113i | ||||
\(179\) | 4.33013 | − | 2.50000i | 0.323649 | − | 0.186859i | −0.329369 | − | 0.944201i | \(-0.606836\pi\) |
0.653018 | + | 0.757343i | \(0.273503\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.3205i | − | 1.28742i | −0.765268 | − | 0.643712i | \(-0.777394\pi\) | ||
0.765268 | − | 0.643712i | \(-0.222606\pi\) | |||||||
\(182\) | −10.9019 | + | 16.0981i | −0.808104 | + | 1.19327i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | + | 8.00000i | 0.589768 | + | 0.589768i | ||||
\(185\) | −9.00000 | − | 5.19615i | −0.661693 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.19615 | − | 9.00000i | −0.379980 | − | 0.658145i | ||||
\(188\) | 3.46410i | 0.252646i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | − | 6.00000i | 0.435286 | − | 0.435286i | ||||
\(191\) | 6.06218 | − | 3.50000i | 0.438644 | − | 0.253251i | −0.264378 | − | 0.964419i | \(-0.585167\pi\) |
0.703022 | + | 0.711168i | \(0.251833\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.50000 | − | 7.79423i | 0.323917 | − | 0.561041i | −0.657376 | − | 0.753563i | \(-0.728333\pi\) |
0.981293 | + | 0.192522i | \(0.0616668\pi\) | |||||||
\(194\) | 1.73205 | − | 1.73205i | 0.124354 | − | 0.124354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.66025 | − | 11.0000i | 0.618590 | − | 0.785714i | ||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.866025 | + | 1.50000i | 0.0613909 | + | 0.106332i | 0.895087 | − | 0.445891i | \(-0.147113\pi\) |
−0.833696 | + | 0.552223i | \(0.813780\pi\) | |||||||
\(200\) | 14.0000 | − | 14.0000i | 0.989949 | − | 0.989949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23.6603 | − | 6.33975i | −1.66473 | − | 0.446063i | ||||
\(203\) | −12.9904 | + | 2.50000i | −0.911746 | + | 0.175466i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.0000 | + | 10.3923i | 1.24808 | + | 0.720577i | ||||
\(209\) | −3.00000 | − | 1.73205i | −0.207514 | − | 0.119808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.6506 | + | 12.5000i | −1.49049 | + | 0.860535i | −0.999941 | − | 0.0108774i | \(-0.996538\pi\) |
−0.490550 | + | 0.871413i | \(0.663204\pi\) | |||||||
\(212\) | − | 2.00000i | − | 0.137361i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.00000 | + | 7.00000i | −0.478510 | + | 0.478510i | ||||
\(215\) | −19.0526 | + | 33.0000i | −1.29937 | + | 2.25058i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.5000 | + | 2.59808i | −0.916440 | + | 0.176369i | ||||
\(218\) | −4.09808 | + | 1.09808i | −0.277557 | + | 0.0743711i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.0000 | − | 6.92820i | −0.809040 | − | 0.467099i | ||||
\(221\) | 13.5000 | − | 23.3827i | 0.908108 | − | 1.57289i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.79423 | − | 13.5000i | 0.521940 | − | 0.904027i | −0.477734 | − | 0.878504i | \(-0.658542\pi\) |
0.999674 | − | 0.0255224i | \(-0.00812491\pi\) | |||||||
\(224\) | −12.3923 | − | 8.39230i | −0.827996 | − | 0.560734i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25.9545 | − | 6.95448i | 1.72647 | − | 0.462605i | ||||
\(227\) | 6.92820 | 0.459841 | 0.229920 | − | 0.973209i | \(-0.426153\pi\) | ||||
0.229920 | + | 0.973209i | \(0.426153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.46410i | 0.228914i | 0.993428 | + | 0.114457i | \(0.0365129\pi\) | ||||
−0.993428 | + | 0.114457i | \(0.963487\pi\) | |||||||
\(230\) | 5.07180 | − | 18.9282i | 0.334424 | − | 1.24809i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.66025 | + | 13.6603i | 0.240307 | + | 0.896840i | ||||
\(233\) | 0.500000 | − | 0.866025i | 0.0327561 | − | 0.0567352i | −0.849183 | − | 0.528099i | \(-0.822905\pi\) |
0.881939 | + | 0.471364i | \(0.156238\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.19615 | − | 3.00000i | 0.338960 | − | 0.195698i | ||||
\(236\) | −3.00000 | + | 1.73205i | −0.195283 | + | 0.112747i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.9019 | + | 16.0981i | −0.706667 | + | 1.04348i | ||||
\(239\) | −9.52628 | + | 5.50000i | −0.616204 | + | 0.355765i | −0.775390 | − | 0.631483i | \(-0.782446\pi\) |
0.159186 | + | 0.987249i | \(0.449113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.46410i | 0.223142i | 0.993756 | + | 0.111571i | \(0.0355883\pi\) | ||||
−0.993756 | + | 0.111571i | \(0.964412\pi\) | |||||||
\(242\) | 2.56218 | − | 9.56218i | 0.164703 | − | 0.614680i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.3923 | −0.665299 | ||||||||
\(245\) | −24.0000 | − | 3.46410i | −1.53330 | − | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 9.00000i | − | 0.572656i | ||||||
\(248\) | 3.80385 | + | 14.1962i | 0.241545 | + | 0.901457i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.46410 | − | 2.53590i | −0.598562 | − | 0.160384i | ||||
\(251\) | 3.46410 | 0.218652 | 0.109326 | − | 0.994006i | \(-0.465131\pi\) | ||||
0.109326 | + | 0.994006i | \(0.465131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | −8.19615 | − | 2.19615i | −0.514272 | − | 0.137799i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 13.8564i | 0.864339i | 0.901792 | + | 0.432169i | \(0.142252\pi\) | ||||
−0.901792 | + | 0.432169i | \(0.857748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.79423 | − | 1.50000i | 0.484310 | − | 0.0932055i | ||||
\(260\) | − | 36.0000i | − | 2.23263i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.07180 | − | 18.9282i | 0.313337 | − | 1.16939i | ||||
\(263\) | 26.0000i | 1.60323i | 0.597841 | + | 0.801614i | \(0.296025\pi\) | ||||
−0.597841 | + | 0.801614i | \(0.703975\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | + | 1.73205i | −0.184289 | + | 0.106399i | ||||
\(266\) | −0.464102 | + | 6.46410i | −0.0284559 | + | 0.396339i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.00000 | + | 15.5885i | 0.549762 | + | 0.952217i | ||||
\(269\) | −25.5000 | + | 14.7224i | −1.55476 | + | 0.897643i | −0.557019 | + | 0.830500i | \(0.688055\pi\) |
−0.997743 | + | 0.0671428i | \(0.978612\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.59808 | − | 4.50000i | 0.157822 | − | 0.273356i | −0.776261 | − | 0.630412i | \(-0.782886\pi\) |
0.934083 | + | 0.357056i | \(0.116219\pi\) | |||||||
\(272\) | 18.0000 | + | 10.3923i | 1.09141 | + | 0.630126i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.92820 | + | 10.9282i | −0.176899 | + | 0.660197i | ||||
\(275\) | 14.0000i | 0.844232i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00000 | −0.240337 | −0.120168 | − | 0.992754i | \(-0.538343\pi\) | ||||
−0.120168 | + | 0.992754i | \(0.538343\pi\) | |||||||
\(278\) | 30.7583 | − | 8.24167i | 1.84476 | − | 0.494303i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.85641 | + | 25.8564i | −0.110942 | + | 1.54522i | ||||
\(281\) | −2.50000 | + | 4.33013i | −0.149137 | + | 0.258314i | −0.930909 | − | 0.365251i | \(-0.880983\pi\) |
0.781771 | + | 0.623565i | \(0.214316\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.33013 | + | 7.50000i | −0.257399 | + | 0.445829i | −0.965544 | − | 0.260238i | \(-0.916199\pi\) |
0.708145 | + | 0.706067i | \(0.249532\pi\) | |||||||
\(284\) | 2.00000 | − | 3.46410i | 0.118678 | − | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.1962 | + | 3.80385i | −0.839436 | + | 0.224926i | ||||
\(287\) | 4.33013 | + | 1.50000i | 0.255599 | + | 0.0885422i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | − | 8.66025i | 0.294118 | − | 0.509427i | ||||
\(290\) | 17.3205 | − | 17.3205i | 1.01710 | − | 1.01710i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 24.2487 | 1.41905 | ||||||||
\(293\) | −4.50000 | + | 2.59808i | −0.262893 | + | 0.151781i | −0.625653 | − | 0.780101i | \(-0.715168\pi\) |
0.362761 | + | 0.931882i | \(0.381834\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.19615 | + | 3.00000i | 0.302532 | + | 0.174667i | ||||
\(296\) | −2.19615 | − | 8.19615i | −0.127649 | − | 0.476392i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.46410 | − | 5.46410i | 0.0848131 | − | 0.316527i | ||||
\(299\) | −10.3923 | − | 18.0000i | −0.601003 | − | 1.04097i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.50000 | − | 28.5788i | −0.317015 | − | 1.64726i | ||||
\(302\) | 19.1244 | + | 5.12436i | 1.10048 | + | 0.294874i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.92820 | 0.397360 | ||||||||
\(305\) | 9.00000 | + | 15.5885i | 0.515339 | + | 0.892592i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.3205 | −0.988534 | −0.494267 | − | 0.869310i | \(-0.664563\pi\) | ||||
−0.494267 | + | 0.869310i | \(0.664563\pi\) | |||||||
\(308\) | 10.3923 | − | 2.00000i | 0.592157 | − | 0.113961i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.0000 | − | 18.0000i | 1.02233 | − | 1.02233i | ||||
\(311\) | −11.2583 | + | 19.5000i | −0.638401 | + | 1.10574i | 0.347382 | + | 0.937724i | \(0.387071\pi\) |
−0.985784 | + | 0.168020i | \(0.946263\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5000 | − | 11.2583i | 1.10221 | − | 0.636358i | 0.165406 | − | 0.986226i | \(-0.447107\pi\) |
0.936799 | + | 0.349867i | \(0.113773\pi\) | |||||||
\(314\) | −12.1244 | + | 12.1244i | −0.684217 | + | 0.684217i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.00000 | 0.337526 | ||||||||
\(317\) | 9.50000 | + | 16.4545i | 0.533573 | + | 0.924176i | 0.999231 | + | 0.0392110i | \(0.0124844\pi\) |
−0.465658 | + | 0.884965i | \(0.654182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.66025 | − | 5.00000i | −0.484881 | − | 0.279946i | ||||
\(320\) | 27.7128 | 1.54919 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.53590 | + | 13.4641i | 0.364231 | + | 0.750325i | ||||
\(323\) | − | 9.00000i | − | 0.500773i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −31.5000 | + | 18.1865i | −1.74731 | + | 1.00881i | ||||
\(326\) | −9.00000 | + | 9.00000i | −0.498464 | + | 0.498464i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.26795 | − | 4.73205i | 0.0700108 | − | 0.261284i | ||||
\(329\) | −1.50000 | + | 4.33013i | −0.0826977 | + | 0.238728i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.866025 | − | 0.500000i | 0.0476011 | − | 0.0274825i | −0.476011 | − | 0.879440i | \(-0.657918\pi\) |
0.523612 | + | 0.851957i | \(0.324584\pi\) | |||||||
\(332\) | 9.00000 | − | 5.19615i | 0.493939 | − | 0.285176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.09808 | + | 1.90192i | −0.388389 | + | 0.104069i | ||||
\(335\) | 15.5885 | − | 27.0000i | 0.851688 | − | 1.47517i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5000 | + | 23.3827i | 0.735392 | + | 1.27374i | 0.954551 | + | 0.298047i | \(0.0963352\pi\) |
−0.219159 | + | 0.975689i | \(0.570331\pi\) | |||||||
\(338\) | −14.0000 | − | 14.0000i | −0.761500 | − | 0.761500i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 36.0000i | − | 1.95237i | ||||||
\(341\) | −9.00000 | − | 5.19615i | −0.487377 | − | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | −30.0526 | + | 8.05256i | −1.62033 | + | 0.434165i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.97372 | − | 26.0263i | −0.374910 | − | 1.39918i | ||||
\(347\) | −25.1147 | − | 14.5000i | −1.34823 | − | 0.778401i | −0.360231 | − | 0.932863i | \(-0.617302\pi\) |
−0.987999 | + | 0.154462i | \(0.950635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.5000 | + | 7.79423i | 0.722638 | + | 0.417215i | 0.815723 | − | 0.578443i | \(-0.196339\pi\) |
−0.0930846 | + | 0.995658i | \(0.529673\pi\) | |||||||
\(350\) | 23.5622 | − | 11.4378i | 1.25945 | − | 0.611377i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.92820 | − | 10.9282i | −0.156074 | − | 0.582475i | ||||
\(353\) | 10.3923i | 0.553127i | 0.960996 | + | 0.276563i | \(0.0891955\pi\) | ||||
−0.960996 | + | 0.276563i | \(0.910804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.92820 | −0.367711 | ||||||||
\(356\) | 8.66025 | + | 15.0000i | 0.458993 | + | 0.794998i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.83013 | − | 6.83013i | −0.0967252 | − | 0.360983i | ||||
\(359\) | 14.7224 | + | 8.50000i | 0.777020 | + | 0.448613i | 0.835373 | − | 0.549683i | \(-0.185252\pi\) |
−0.0583530 | + | 0.998296i | \(0.518585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.00000 | + | 13.8564i | 0.421053 | + | 0.729285i | ||||
\(362\) | −23.6603 | − | 6.33975i | −1.24356 | − | 0.333210i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.0000 | + | 20.7846i | 0.943456 | + | 1.08941i | ||||
\(365\) | −21.0000 | − | 36.3731i | −1.09919 | − | 1.90385i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.6410 | −1.80825 | −0.904123 | − | 0.427272i | \(-0.859475\pi\) | ||||
−0.904123 | + | 0.427272i | \(0.859475\pi\) | |||||||
\(368\) | 13.8564 | − | 8.00000i | 0.722315 | − | 0.417029i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.3923 | + | 10.3923i | −0.540270 | + | 0.540270i | ||||
\(371\) | 0.866025 | − | 2.50000i | 0.0449618 | − | 0.129794i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.0000 | −1.34623 | −0.673114 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673114 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(374\) | −14.1962 | + | 3.80385i | −0.734066 | + | 0.196692i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.73205 | + | 1.26795i | 0.244037 | + | 0.0653895i | ||||
\(377\) | − | 25.9808i | − | 1.33808i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.0000i | 0.719132i | 0.933120 | + | 0.359566i | \(0.117075\pi\) | ||||
−0.933120 | + | 0.359566i | \(0.882925\pi\) | |||||||
\(380\) | −6.00000 | − | 10.3923i | −0.307794 | − | 0.533114i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.56218 | − | 9.56218i | −0.131092 | − | 0.489244i | ||||
\(383\) | 6.92820 | 0.354015 | 0.177007 | − | 0.984210i | \(-0.443358\pi\) | ||||
0.177007 | + | 0.984210i | \(0.443358\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | − | 13.8564i | −0.611577 | − | 0.706188i | ||||
\(386\) | −9.00000 | − | 9.00000i | −0.458088 | − | 0.458088i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.73205 | − | 3.00000i | −0.0879316 | − | 0.152302i | ||||
\(389\) | 32.0000 | 1.62246 | 0.811232 | − | 0.584724i | \(-0.198797\pi\) | ||||
0.811232 | + | 0.584724i | \(0.198797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3923 | − | 18.0000i | −0.525561 | − | 0.910299i | ||||
\(392\) | −11.8564 | − | 15.8564i | −0.598839 | − | 0.800869i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.66025 | − | 13.6603i | 0.184401 | − | 0.688194i | ||||
\(395\) | −5.19615 | − | 9.00000i | −0.261447 | − | 0.452839i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5000 | − | 9.52628i | −0.828111 | − | 0.478110i | 0.0250943 | − | 0.999685i | \(-0.492011\pi\) |
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | 2.36603 | − | 0.633975i | 0.118598 | − | 0.0317783i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.0000 | − | 24.2487i | −0.700000 | − | 1.21244i | ||||
\(401\) | −8.00000 | −0.399501 | −0.199750 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199750 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 27.0000i | − | 1.34497i | ||||||
\(404\) | −17.3205 | + | 30.0000i | −0.861727 | + | 1.49256i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.33975 | + | 18.6603i | −0.0664905 | + | 0.926093i | ||||
\(407\) | 5.19615 | + | 3.00000i | 0.257564 | + | 0.148704i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.5000 | + | 7.79423i | 0.667532 | + | 0.385400i | 0.795141 | − | 0.606425i | \(-0.207397\pi\) |
−0.127609 | + | 0.991825i | \(0.540730\pi\) | |||||||
\(410\) | −8.19615 | + | 2.19615i | −0.404779 | + | 0.108460i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.50000 | + | 0.866025i | −0.221431 | + | 0.0426143i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.5885 | − | 9.00000i | −0.765207 | − | 0.441793i | ||||
\(416\) | 20.7846 | − | 20.7846i | 1.01905 | − | 1.01905i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.46410 | + | 3.46410i | −0.169435 | + | 0.169435i | ||||
\(419\) | 7.79423 | + | 13.5000i | 0.380773 | + | 0.659518i | 0.991173 | − | 0.132575i | \(-0.0423246\pi\) |
−0.610400 | + | 0.792093i | \(0.708991\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.5000 | − | 19.9186i | 0.560476 | − | 0.970772i | −0.436979 | − | 0.899472i | \(-0.643952\pi\) |
0.997455 | − | 0.0713008i | \(-0.0227150\pi\) | |||||||
\(422\) | 9.15064 | + | 34.1506i | 0.445446 | + | 1.66243i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.73205 | − | 0.732051i | −0.132680 | − | 0.0355515i | ||||
\(425\) | −31.5000 | + | 18.1865i | −1.52797 | + | 0.882176i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.9904 | − | 4.50000i | −0.628649 | − | 0.217770i | ||||
\(428\) | 7.00000 | + | 12.1244i | 0.338358 | + | 0.586053i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 38.1051 | + | 38.1051i | 1.83759 | + | 1.83759i | ||||
\(431\) | −4.33013 | + | 2.50000i | −0.208575 | + | 0.120421i | −0.600649 | − | 0.799513i | \(-0.705091\pi\) |
0.392074 | + | 0.919934i | \(0.371758\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.7128i | − | 1.33179i | −0.746044 | − | 0.665896i | \(-0.768049\pi\) | ||
0.746044 | − | 0.665896i | \(-0.231951\pi\) | |||||||
\(434\) | −1.39230 | + | 19.3923i | −0.0668328 | + | 0.930860i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.00000i | 0.287348i | ||||||||
\(437\) | −6.00000 | − | 3.46410i | −0.287019 | − | 0.165710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.06218 | − | 10.5000i | −0.289332 | − | 0.501138i | 0.684318 | − | 0.729183i | \(-0.260100\pi\) |
−0.973650 | + | 0.228046i | \(0.926766\pi\) | |||||||
\(440\) | −13.8564 | + | 13.8564i | −0.660578 | + | 0.660578i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −27.0000 | − | 27.0000i | −1.28426 | − | 1.28426i | ||||
\(443\) | −26.8468 | + | 15.5000i | −1.27553 | + | 0.736427i | −0.976023 | − | 0.217667i | \(-0.930155\pi\) |
−0.299506 | + | 0.954094i | \(0.596822\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0000 | − | 25.9808i | 0.711068 | − | 1.23161i | ||||
\(446\) | −15.5885 | − | 15.5885i | −0.738135 | − | 0.738135i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.0000 | + | 13.8564i | −0.755929 | + | 0.654654i | ||||
\(449\) | 26.0000 | 1.22702 | 0.613508 | − | 0.789689i | \(-0.289758\pi\) | ||||
0.613508 | + | 0.789689i | \(0.289758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.73205 | + | 3.00000i | 0.0815591 | + | 0.141264i | ||||
\(452\) | − | 38.0000i | − | 1.78737i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.53590 | − | 9.46410i | 0.119016 | − | 0.444172i | ||||
\(455\) | 15.5885 | − | 45.0000i | 0.730798 | − | 2.10963i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.50000 | − | 2.59808i | −0.0701670 | − | 0.121533i | 0.828807 | − | 0.559534i | \(-0.189020\pi\) |
−0.898974 | + | 0.438001i | \(0.855687\pi\) | |||||||
\(458\) | 4.73205 | + | 1.26795i | 0.221114 | + | 0.0592474i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −24.0000 | − | 13.8564i | −1.11901 | − | 0.646058i | ||||
\(461\) | −28.5000 | − | 16.4545i | −1.32738 | − | 0.766362i | −0.342484 | − | 0.939524i | \(-0.611268\pi\) |
−0.984893 | + | 0.173162i | \(0.944602\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.5788 | + | 16.5000i | −1.32817 | + | 0.766820i | −0.985017 | − | 0.172459i | \(-0.944829\pi\) |
−0.343155 | + | 0.939279i | \(0.611495\pi\) | |||||||
\(464\) | 20.0000 | 0.928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.00000 | − | 1.00000i | −0.0463241 | − | 0.0463241i | ||||
\(467\) | 0.866025 | − | 1.50000i | 0.0400749 | − | 0.0694117i | −0.845292 | − | 0.534304i | \(-0.820574\pi\) |
0.885367 | + | 0.464892i | \(0.153907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.50000 | + | 23.3827i | 0.207791 | + | 1.07971i | ||||
\(470\) | −2.19615 | − | 8.19615i | −0.101301 | − | 0.378060i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.26795 | + | 4.73205i | 0.0583621 | + | 0.217810i | ||||
\(473\) | 11.0000 | − | 19.0526i | 0.505781 | − | 0.876038i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.06218 | + | 10.5000i | −0.278152 | + | 0.481773i | ||||
\(476\) | 18.0000 | + | 20.7846i | 0.825029 | + | 0.952661i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.02628 | + | 15.0263i | 0.184158 | + | 0.687286i | ||||
\(479\) | −20.7846 | −0.949673 | −0.474837 | − | 0.880074i | \(-0.657493\pi\) | ||||
−0.474837 | + | 0.880074i | \(0.657493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.5885i | 0.710772i | ||||||||
\(482\) | 4.73205 | + | 1.26795i | 0.215539 | + | 0.0577535i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.1244 | − | 7.00000i | −0.551107 | − | 0.318182i | ||||
\(485\) | −3.00000 | + | 5.19615i | −0.136223 | + | 0.235945i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.9186 | + | 11.5000i | −0.902597 | + | 0.521115i | −0.878042 | − | 0.478584i | \(-0.841150\pi\) |
−0.0245553 | + | 0.999698i | \(0.507817\pi\) | |||||||
\(488\) | −3.80385 | + | 14.1962i | −0.172192 | + | 0.642630i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.5167 | + | 31.5167i | −0.610620 | + | 1.42378i | ||||
\(491\) | 16.4545 | − | 9.50000i | 0.742580 | − | 0.428729i | −0.0804264 | − | 0.996761i | \(-0.525628\pi\) |
0.823007 | + | 0.568032i | \(0.192295\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 25.9808i | − | 1.17011i | ||||||
\(494\) | −12.2942 | − | 3.29423i | −0.553143 | − | 0.148214i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.7846 | 0.933257 | ||||||||
\(497\) | 4.00000 | − | 3.46410i | 0.179425 | − | 0.155386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.00000i | 0.0895323i | 0.998997 | + | 0.0447661i | \(0.0142543\pi\) | ||||
−0.998997 | + | 0.0447661i | \(0.985746\pi\) | |||||||
\(500\) | −6.92820 | + | 12.0000i | −0.309839 | + | 0.536656i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.26795 | − | 4.73205i | 0.0565913 | − | 0.211202i | ||||
\(503\) | 41.5692 | 1.85348 | 0.926740 | − | 0.375703i | \(-0.122599\pi\) | ||||
0.926740 | + | 0.375703i | \(0.122599\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 60.0000 | 2.66996 | ||||||||
\(506\) | −2.92820 | + | 10.9282i | −0.130175 | + | 0.485818i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.00000 | + | 10.3923i | −0.266207 | + | 0.461084i | ||||
\(509\) | − | 6.92820i | − | 0.307087i | −0.988142 | − | 0.153544i | \(-0.950931\pi\) | ||
0.988142 | − | 0.153544i | \(-0.0490686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.3109 | + | 10.5000i | 1.34087 | + | 0.464493i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.9282 | + | 5.07180i | 0.834887 | + | 0.223707i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00000 | + | 1.73205i | −0.131940 | + | 0.0761755i | ||||
\(518\) | 0.803848 | − | 11.1962i | 0.0353190 | − | 0.491931i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −49.1769 | − | 13.1769i | −2.15655 | − | 0.577846i | ||||
\(521\) | 19.5000 | − | 11.2583i | 0.854311 | − | 0.493236i | −0.00779240 | − | 0.999970i | \(-0.502480\pi\) |
0.862103 | + | 0.506733i | \(0.169147\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.4545 | + | 28.5000i | −0.719504 | + | 1.24622i | 0.241692 | + | 0.970353i | \(0.422298\pi\) |
−0.961196 | + | 0.275865i | \(0.911036\pi\) | |||||||
\(524\) | −24.0000 | − | 13.8564i | −1.04844 | − | 0.605320i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.5167 | + | 9.51666i | 1.54860 | + | 0.414946i | ||||
\(527\) | − | 27.0000i | − | 1.17614i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 1.26795 | + | 4.73205i | 0.0550762 | + | 0.205547i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.66025 | + | 3.00000i | 0.375470 | + | 0.130066i | ||||
\(533\) | −4.50000 | + | 7.79423i | −0.194917 | + | 0.337606i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.1244 | − | 21.0000i | 0.524182 | − | 0.907909i | ||||
\(536\) | 24.5885 | − | 6.58846i | 1.06206 | − | 0.284578i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.7776 | + | 40.2224i | 0.464654 | + | 1.73411i | ||||
\(539\) | 13.8564 | + | 2.00000i | 0.596838 | + | 0.0861461i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.5000 | + | 35.5070i | −0.881364 | + | 1.52657i | −0.0315385 | + | 0.999503i | \(0.510041\pi\) |
−0.849825 | + | 0.527064i | \(0.823293\pi\) | |||||||
\(542\) | −5.19615 | − | 5.19615i | −0.223194 | − | 0.223194i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.7846 | − | 20.7846i | 0.891133 | − | 0.891133i | ||||
\(545\) | 9.00000 | − | 5.19615i | 0.385518 | − | 0.222579i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.59808 | − | 1.50000i | −0.111086 | − | 0.0641354i | 0.443428 | − | 0.896310i | \(-0.353762\pi\) |
−0.554513 | + | 0.832175i | \(0.687096\pi\) | |||||||
\(548\) | 13.8564 | + | 8.00000i | 0.591916 | + | 0.341743i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 19.1244 | + | 5.12436i | 0.815465 | + | 0.218503i | ||||
\(551\) | −4.33013 | − | 7.50000i | −0.184470 | − | 0.319511i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.50000 | + | 2.59808i | 0.318932 | + | 0.110481i | ||||
\(554\) | −1.46410 | + | 5.46410i | −0.0622037 | + | 0.232147i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 45.0333i | − | 1.90984i | ||||||
\(557\) | 2.50000 | + | 4.33013i | 0.105928 | + | 0.183473i | 0.914117 | − | 0.405450i | \(-0.132885\pi\) |
−0.808189 | + | 0.588924i | \(0.799552\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 57.1577 | 2.41751 | ||||||||
\(560\) | 34.6410 | + | 12.0000i | 1.46385 | + | 0.507093i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.00000 | + | 5.00000i | 0.210912 | + | 0.210912i | ||||
\(563\) | −11.2583 | + | 19.5000i | −0.474482 | + | 0.821827i | −0.999573 | − | 0.0292191i | \(-0.990698\pi\) |
0.525091 | + | 0.851046i | \(0.324031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −57.0000 | + | 32.9090i | −2.39801 | + | 1.38449i | ||||
\(566\) | 8.66025 | + | 8.66025i | 0.364018 | + | 0.364018i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | − | 4.00000i | −0.167836 | − | 0.167836i | ||||
\(569\) | 0.500000 | + | 0.866025i | 0.0209611 | + | 0.0363057i | 0.876316 | − | 0.481737i | \(-0.159994\pi\) |
−0.855355 | + | 0.518043i | \(0.826661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.3827 | + | 13.5000i | 0.978535 | + | 0.564957i | 0.901828 | − | 0.432096i | \(-0.142226\pi\) |
0.0767074 | + | 0.997054i | \(0.475559\pi\) | |||||||
\(572\) | 20.7846i | 0.869048i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.63397 | − | 5.36603i | 0.151679 | − | 0.223974i | ||||
\(575\) | 28.0000i | 1.16768i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5000 | − | 11.2583i | 0.811796 | − | 0.468690i | −0.0357834 | − | 0.999360i | \(-0.511393\pi\) |
0.847579 | + | 0.530669i | \(0.178059\pi\) | |||||||
\(578\) | −10.0000 | − | 10.0000i | −0.415945 | − | 0.415945i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −17.3205 | − | 30.0000i | −0.719195 | − | 1.24568i | ||||
\(581\) | 13.5000 | − | 2.59808i | 0.560074 | − | 0.107786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.73205 | − | 1.00000i | 0.0717342 | − | 0.0414158i | ||||
\(584\) | 8.87564 | − | 33.1244i | 0.367277 | − | 1.37070i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.90192 | + | 7.09808i | 0.0785677 | + | 0.293219i | ||||
\(587\) | 16.4545 | − | 28.5000i | 0.679149 | − | 1.17632i | −0.296088 | − | 0.955161i | \(-0.595682\pi\) |
0.975237 | − | 0.221160i | \(-0.0709844\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.50000 | − | 7.79423i | −0.185419 | − | 0.321156i | ||||
\(590\) | 6.00000 | − | 6.00000i | 0.247016 | − | 0.247016i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0000 | −0.493197 | ||||||||
\(593\) | 13.5000 | + | 7.79423i | 0.554379 | + | 0.320071i | 0.750886 | − | 0.660432i | \(-0.229627\pi\) |
−0.196508 | + | 0.980502i | \(0.562960\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.5885 | − | 45.0000i | 0.639064 | − | 1.84482i | ||||
\(596\) | −6.92820 | − | 4.00000i | −0.283790 | − | 0.163846i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −28.3923 | + | 7.60770i | −1.16105 | + | 0.311102i | ||||
\(599\) | 19.9186 | + | 11.5000i | 0.813851 | + | 0.469877i | 0.848292 | − | 0.529529i | \(-0.177632\pi\) |
−0.0344402 | + | 0.999407i | \(0.510965\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.50000 | − | 0.866025i | −0.0611863 | − | 0.0353259i | 0.469095 | − | 0.883148i | \(-0.344580\pi\) |
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | −41.0526 | − | 2.94744i | −1.67318 | − | 0.120129i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.0000 | − | 24.2487i | 0.569652 | − | 0.986666i | ||||
\(605\) | 24.2487i | 0.985850i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.7128 | 1.12483 | 0.562414 | − | 0.826856i | \(-0.309873\pi\) | ||||
0.562414 | + | 0.826856i | \(0.309873\pi\) | |||||||
\(608\) | 2.53590 | − | 9.46410i | 0.102844 | − | 0.383820i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.5885 | − | 6.58846i | 0.995558 | − | 0.266759i | ||||
\(611\) | −7.79423 | − | 4.50000i | −0.315321 | − | 0.182051i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.50000 | − | 9.52628i | −0.222143 | − | 0.384763i | 0.733316 | − | 0.679888i | \(-0.237972\pi\) |
−0.955458 | + | 0.295126i | \(0.904638\pi\) | |||||||
\(614\) | −6.33975 | + | 23.6603i | −0.255851 | + | 0.954850i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.07180 | − | 14.9282i | 0.0431839 | − | 0.601474i | ||||
\(617\) | 6.50000 | + | 11.2583i | 0.261680 | + | 0.453243i | 0.966689 | − | 0.255956i | \(-0.0823901\pi\) |
−0.705008 | + | 0.709199i | \(0.749057\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.8564 | −0.556936 | −0.278468 | − | 0.960446i | \(-0.589827\pi\) | ||||
−0.278468 | + | 0.960446i | \(0.589827\pi\) | |||||||
\(620\) | −18.0000 | − | 31.1769i | −0.722897 | − | 1.25210i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.5167 | + | 22.5167i | 0.902836 | + | 0.902836i | ||||
\(623\) | 4.33013 | + | 22.5000i | 0.173483 | + | 0.901443i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −8.24167 | − | 30.7583i | −0.329403 | − | 1.22935i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.1244 | + | 21.0000i | 0.483814 | + | 0.837991i | ||||
\(629\) | 15.5885i | 0.621552i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.0000i | 1.19428i | 0.802137 | + | 0.597141i | \(0.203697\pi\) | ||||
−0.802137 | + | 0.597141i | \(0.796303\pi\) | |||||||
\(632\) | 2.19615 | − | 8.19615i | 0.0873583 | − | 0.326025i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.9545 | − | 6.95448i | 1.03078 | − | 0.276198i | ||||
\(635\) | 20.7846 | 0.824812 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.5000 | + | 33.7750i | 0.534889 | + | 1.33821i | ||||
\(638\) | −10.0000 | + | 10.0000i | −0.395904 | + | 0.395904i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.1436 | − | 37.8564i | 0.400961 | − | 1.49641i | ||||
\(641\) | −4.00000 | −0.157991 | −0.0789953 | − | 0.996875i | \(-0.525171\pi\) | ||||
−0.0789953 | + | 0.996875i | \(0.525171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.79423 | + | 13.5000i | 0.307374 | + | 0.532388i | 0.977787 | − | 0.209600i | \(-0.0672163\pi\) |
−0.670413 | + | 0.741988i | \(0.733883\pi\) | |||||||
\(644\) | 20.7846 | − | 4.00000i | 0.819028 | − | 0.157622i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.2942 | − | 3.29423i | −0.483710 | − | 0.129610i | ||||
\(647\) | −7.79423 | − | 13.5000i | −0.306423 | − | 0.530740i | 0.671154 | − | 0.741318i | \(-0.265799\pi\) |
−0.977577 | + | 0.210578i | \(0.932465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.00000 | − | 1.73205i | −0.117760 | − | 0.0679889i | ||||
\(650\) | 13.3135 | + | 49.6865i | 0.522197 | + | 1.94887i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.00000 | + | 15.5885i | 0.352467 | + | 0.610491i | ||||
\(653\) | −26.0000 | −1.01746 | −0.508729 | − | 0.860927i | \(-0.669885\pi\) | ||||
−0.508729 | + | 0.860927i | \(0.669885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.0000i | 1.87552i | ||||||||
\(656\) | −6.00000 | − | 3.46410i | −0.234261 | − | 0.135250i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.36603 | + | 3.63397i | 0.209189 | + | 0.141667i | ||||
\(659\) | 16.4545 | + | 9.50000i | 0.640976 | + | 0.370067i | 0.784990 | − | 0.619508i | \(-0.212668\pi\) |
−0.144015 | + | 0.989576i | \(0.546001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.5000 | + | 6.06218i | 0.408403 | + | 0.235791i | 0.690103 | − | 0.723711i | \(-0.257565\pi\) |
−0.281701 | + | 0.959502i | \(0.590898\pi\) | |||||||
\(662\) | −0.366025 | − | 1.36603i | −0.0142260 | − | 0.0530921i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.80385 | − | 14.1962i | −0.147618 | − | 0.550918i | ||||
\(665\) | −3.00000 | − | 15.5885i | −0.116335 | − | 0.604494i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.3205 | − | 10.0000i | −0.670653 | − | 0.387202i | ||||
\(668\) | 10.3923i | 0.402090i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −31.1769 | − | 31.1769i | −1.20447 | − | 1.20447i | ||||
\(671\) | −5.19615 | − | 9.00000i | −0.200595 | − | 0.347441i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.5000 | + | 33.7750i | −0.751670 | + | 1.30193i | 0.195343 | + | 0.980735i | \(0.437418\pi\) |
−0.947013 | + | 0.321195i | \(0.895915\pi\) | |||||||
\(674\) | 36.8827 | − | 9.88269i | 1.42067 | − | 0.380667i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.2487 | + | 14.0000i | −0.932643 | + | 0.538462i | ||||
\(677\) | 19.5000 | − | 11.2583i | 0.749446 | − | 0.432693i | −0.0760478 | − | 0.997104i | \(-0.524230\pi\) |
0.825494 | + | 0.564411i | \(0.190897\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.866025 | − | 4.50000i | −0.0332350 | − | 0.172694i | ||||
\(680\) | −49.1769 | − | 13.1769i | −1.88585 | − | 0.505312i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.3923 | + | 10.3923i | −0.397942 | + | 0.397942i | ||||
\(683\) | −40.7032 | + | 23.5000i | −1.55746 | + | 0.899203i | −0.559966 | + | 0.828516i | \(0.689186\pi\) |
−0.997499 | + | 0.0706868i | \(0.977481\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 27.7128i | − | 1.05885i | ||||||
\(686\) | −7.95448 | − | 24.9545i | −0.303704 | − | 0.952767i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 44.0000i | 1.67748i | ||||||||
\(689\) | 4.50000 | + | 2.59808i | 0.171436 | + | 0.0989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.7224 | + | 25.5000i | 0.560068 | + | 0.970066i | 0.997490 | + | 0.0708094i | \(0.0225582\pi\) |
−0.437422 | + | 0.899256i | \(0.644108\pi\) | |||||||
\(692\) | −38.1051 | −1.44854 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.0000 | + | 29.0000i | −1.10082 | + | 1.10082i | ||||
\(695\) | −67.5500 | + | 39.0000i | −2.56232 | + | 1.47935i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.50000 | + | 7.79423i | −0.170450 | + | 0.295227i | ||||
\(698\) | 15.5885 | − | 15.5885i | 0.590032 | − | 0.590032i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.00000 | − | 36.3731i | −0.264575 | − | 1.37477i | ||||
\(701\) | 16.0000 | 0.604312 | 0.302156 | − | 0.953259i | \(-0.402294\pi\) | ||||
0.302156 | + | 0.953259i | \(0.402294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.59808 | + | 4.50000i | 0.0979883 | + | 0.169721i | ||||
\(704\) | −16.0000 | −0.603023 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.1962 | + | 3.80385i | 0.534279 | + | 0.143160i | ||||
\(707\) | −34.6410 | + | 30.0000i | −1.30281 | + | 1.12827i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.5000 | + | 28.5788i | 0.619671 | + | 1.07330i | 0.989546 | + | 0.144219i | \(0.0460671\pi\) |
−0.369875 | + | 0.929081i | \(0.620600\pi\) | |||||||
\(710\) | −2.53590 | + | 9.46410i | −0.0951706 | + | 0.355181i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 23.6603 | − | 6.33975i | 0.886706 | − | 0.237592i | ||||
\(713\) | −18.0000 | − | 10.3923i | −0.674105 | − | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.1769 | − | 18.0000i | 1.16595 | − | 0.673162i | ||||
\(716\) | −10.0000 | −0.373718 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.0000 | − | 17.0000i | 0.634434 | − | 0.634434i | ||||
\(719\) | 9.52628 | − | 16.5000i | 0.355270 | − | 0.615346i | −0.631894 | − | 0.775055i | \(-0.717722\pi\) |
0.987164 | + | 0.159709i | \(0.0510555\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 21.8564 | − | 5.85641i | 0.813411 | − | 0.217953i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.3205 | + | 30.0000i | −0.643712 | + | 1.11494i | ||||
\(725\) | −17.5000 | + | 30.3109i | −0.649934 | + | 1.12572i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.33013 | − | 7.50000i | 0.160596 | − | 0.278160i | −0.774487 | − | 0.632590i | \(-0.781992\pi\) |
0.935082 | + | 0.354430i | \(0.115325\pi\) | |||||||
\(728\) | 34.9808 | − | 16.9808i | 1.29647 | − | 0.629349i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −57.3731 | + | 15.3731i | −2.12347 | + | 0.568983i | ||||
\(731\) | 57.1577 | 2.11405 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 20.7846i | − | 0.767697i | −0.923396 | − | 0.383849i | \(-0.874598\pi\) | ||
0.923396 | − | 0.383849i | \(-0.125402\pi\) | |||||||
\(734\) | −12.6795 | + | 47.3205i | −0.468009 | + | 1.74663i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.85641 | − | 21.8564i | −0.215870 | − | 0.805638i | ||||
\(737\) | −9.00000 | + | 15.5885i | −0.331519 | + | 0.574208i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.1673 | − | 25.5000i | 1.62472 | − | 0.938033i | 0.639087 | − | 0.769135i | \(-0.279313\pi\) |
0.985634 | − | 0.168898i | \(-0.0540208\pi\) | |||||||
\(740\) | 10.3923 | + | 18.0000i | 0.382029 | + | 0.661693i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.09808 | − | 2.09808i | −0.113734 | − | 0.0770228i | ||||
\(743\) | −25.1147 | + | 14.5000i | −0.921370 | + | 0.531953i | −0.884072 | − | 0.467351i | \(-0.845209\pi\) |
−0.0372984 | + | 0.999304i | \(0.511875\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.8564i | 0.507659i | ||||||||
\(746\) | −9.51666 | + | 35.5167i | −0.348430 | + | 1.30036i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.7846i | 0.759961i | ||||||||
\(749\) | 3.50000 | + | 18.1865i | 0.127887 | + | 0.664521i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.00000i | − | 0.0729810i | −0.999334 | − | 0.0364905i | \(-0.988382\pi\) | ||
0.999334 | − | 0.0364905i | \(-0.0116179\pi\) | |||||||
\(752\) | 3.46410 | − | 6.00000i | 0.126323 | − | 0.218797i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −35.4904 | − | 9.50962i | −1.29248 | − | 0.346320i | ||||
\(755\) | −48.4974 | −1.76500 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.0000 | −0.872295 | −0.436147 | − | 0.899875i | \(-0.643657\pi\) | ||||
−0.436147 | + | 0.899875i | \(0.643657\pi\) | |||||||
\(758\) | 19.1244 | + | 5.12436i | 0.694628 | + | 0.186125i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.3923 | + | 4.39230i | −0.594611 | + | 0.159326i | ||||
\(761\) | 10.3923i | 0.376721i | 0.982100 | + | 0.188360i | \(0.0603173\pi\) | ||||
−0.982100 | + | 0.188360i | \(0.939683\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.59808 | + | 7.50000i | −0.0940567 | + | 0.271518i | ||||
\(764\) | −14.0000 | −0.506502 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.53590 | − | 9.46410i | 0.0916257 | − | 0.341952i | ||||
\(767\) | − | 9.00000i | − | 0.324971i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.50000 | + | 4.33013i | −0.270457 | + | 0.156148i | −0.629095 | − | 0.777328i | \(-0.716574\pi\) |
0.358638 | + | 0.933477i | \(0.383241\pi\) | |||||||
\(770\) | −23.3205 | + | 11.3205i | −0.840413 | + | 0.407963i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.5885 | + | 9.00000i | −0.561041 | + | 0.323917i | ||||
\(773\) | −1.50000 | + | 0.866025i | −0.0539513 | + | 0.0311488i | −0.526733 | − | 0.850031i | \(-0.676583\pi\) |
0.472782 | + | 0.881180i | \(0.343250\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.1865 | + | 31.5000i | −0.653280 | + | 1.13151i | ||||
\(776\) | −4.73205 | + | 1.26795i | −0.169871 | + | 0.0455167i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.7128 | − | 43.7128i | 0.419925 | − | 1.56718i | ||||
\(779\) | 3.00000i | 0.107486i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | −28.3923 | + | 7.60770i | −1.01531 | + | 0.272051i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.0000 | + | 10.3923i | −0.928571 | + | 0.371154i | ||||
\(785\) | 21.0000 | − | 36.3731i | 0.749522 | − | 1.29821i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.1147 | − | 43.5000i | 0.895244 | − | 1.55061i | 0.0617409 | − | 0.998092i | \(-0.480335\pi\) |
0.833503 | − | 0.552515i | \(-0.186332\pi\) | |||||||
\(788\) | −17.3205 | − | 10.0000i | −0.617018 | − | 0.356235i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.1962 | + | 3.80385i | −0.505076 | + | 0.135335i | ||||
\(791\) | 16.4545 | − | 47.5000i | 0.585054 | − | 1.68891i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.5000 | − | 23.3827i | 0.479399 | − | 0.830344i | ||||
\(794\) | −19.0526 | + | 19.0526i | −0.676150 | + | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 3.46410i | − | 0.122782i | ||||||
\(797\) | 22.5000 | − | 12.9904i | 0.796991 | − | 0.460143i | −0.0454270 | − | 0.998968i | \(-0.514465\pi\) |
0.842418 | + | 0.538825i | \(0.181132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.79423 | − | 4.50000i | −0.275740 | − | 0.159199i | ||||
\(800\) | −38.2487 | + | 10.2487i | −1.35230 | + | 0.362347i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.92820 | + | 10.9282i | −0.103398 | + | 0.385888i | ||||
\(803\) | 12.1244 | + | 21.0000i | 0.427859 | + | 0.741074i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.0000 | − | 27.7128i | −0.845889 | − | 0.976748i | ||||
\(806\) | −36.8827 | − | 9.88269i | −1.29914 | − | 0.348103i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 34.6410 | + | 34.6410i | 1.21867 | + | 1.21867i | ||||
\(809\) | 11.5000 | + | 19.9186i | 0.404318 | + | 0.700300i | 0.994242 | − | 0.107159i | \(-0.0341754\pi\) |
−0.589923 | + | 0.807459i | \(0.700842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.92820 | 0.243282 | 0.121641 | − | 0.992574i | \(-0.461184\pi\) | ||||
0.121641 | + | 0.992574i | \(0.461184\pi\) | |||||||
\(812\) | 25.0000 | + | 8.66025i | 0.877328 | + | 0.303915i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | − | 6.00000i | 0.210300 | − | 0.210300i | ||||
\(815\) | 15.5885 | − | 27.0000i | 0.546040 | − | 0.945769i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.5000 | − | 9.52628i | 0.577262 | − | 0.333282i | ||||
\(818\) | 15.5885 | − | 15.5885i | 0.545038 | − | 0.545038i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0000i | 0.419058i | ||||||||
\(821\) | −27.5000 | − | 47.6314i | −0.959757 | − | 1.66235i | −0.723087 | − | 0.690757i | \(-0.757277\pi\) |
−0.236670 | − | 0.971590i | \(-0.576056\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.1865 | − | 10.5000i | −0.633943 | − | 0.366007i | 0.148335 | − | 0.988937i | \(-0.452609\pi\) |
−0.782277 | + | 0.622930i | \(0.785942\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.464102 | + | 6.46410i | −0.0161482 | + | 0.224915i | ||||
\(827\) | − | 10.0000i | − | 0.347734i | −0.984769 | − | 0.173867i | \(-0.944374\pi\) | ||
0.984769 | − | 0.173867i | \(-0.0556263\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.5000 | − | 6.06218i | 0.364680 | − | 0.210548i | −0.306452 | − | 0.951886i | \(-0.599142\pi\) |
0.671132 | + | 0.741338i | \(0.265808\pi\) | |||||||
\(830\) | −18.0000 | + | 18.0000i | −0.624789 | + | 0.624789i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.7846 | − | 36.0000i | −0.720577 | − | 1.24808i | ||||
\(833\) | 13.5000 | + | 33.7750i | 0.467747 | + | 1.17023i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.5885 | − | 9.00000i | 0.539461 | − | 0.311458i | ||||
\(836\) | 3.46410 | + | 6.00000i | 0.119808 | + | 0.207514i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.2942 | − | 5.70577i | 0.735597 | − | 0.197103i | ||||
\(839\) | 9.52628 | − | 16.5000i | 0.328884 | − | 0.569643i | −0.653407 | − | 0.757007i | \(-0.726661\pi\) |
0.982291 | + | 0.187364i | \(0.0599943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | + | 3.46410i | 0.0689655 | + | 0.119452i | ||||
\(842\) | −23.0000 | − | 23.0000i | −0.792632 | − | 0.792632i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 50.0000 | 1.72107 | ||||||||
\(845\) | 42.0000 | + | 24.2487i | 1.44484 | + | 0.834181i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.1244 | − | 14.0000i | −0.416598 | − | 0.481046i | ||||
\(848\) | −2.00000 | + | 3.46410i | −0.0686803 | + | 0.118958i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.3135 | + | 49.6865i | 0.456648 | + | 1.70423i | ||||
\(851\) | 10.3923 | + | 6.00000i | 0.356244 | + | 0.205677i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.5000 | − | 12.9904i | −0.770385 | − | 0.444782i | 0.0626267 | − | 0.998037i | \(-0.480052\pi\) |
−0.833012 | + | 0.553255i | \(0.813386\pi\) | |||||||
\(854\) | −10.9019 | + | 16.0981i | −0.373056 | + | 0.550865i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.1244 | − | 5.12436i | 0.653657 | − | 0.175147i | ||||
\(857\) | 24.2487i | 0.828320i | 0.910204 | + | 0.414160i | \(0.135925\pi\) | ||||
−0.910204 | + | 0.414160i | \(0.864075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.7128 | 0.945549 | 0.472774 | − | 0.881183i | \(-0.343253\pi\) | ||||
0.472774 | + | 0.881183i | \(0.343253\pi\) | |||||||
\(860\) | 66.0000 | − | 38.1051i | 2.25058 | − | 1.29937i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.83013 | + | 6.83013i | 0.0623344 | + | 0.232635i | ||||
\(863\) | −30.3109 | − | 17.5000i | −1.03179 | − | 0.595707i | −0.114296 | − | 0.993447i | \(-0.536461\pi\) |
−0.917498 | + | 0.397740i | \(0.869795\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.0000 | + | 57.1577i | 1.12203 | + | 1.94342i | ||||
\(866\) | −37.8564 | − | 10.1436i | −1.28641 | − | 0.344693i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 25.9808 | + | 9.00000i | 0.881845 | + | 0.305480i | ||||
\(869\) | 3.00000 | + | 5.19615i | 0.101768 | + | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.7654 | −1.58458 | ||||||||
\(872\) | 8.19615 | + | 2.19615i | 0.277557 | + | 0.0743711i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.92820 | + | 6.92820i | −0.234350 | + | 0.234350i | ||||
\(875\) | −13.8564 | + | 12.0000i | −0.468432 | + | 0.405674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0000 | 0.540282 | 0.270141 | − | 0.962821i | \(-0.412930\pi\) | ||||
0.270141 | + | 0.962821i | \(0.412930\pi\) | |||||||
\(878\) | −16.5622 | + | 4.43782i | −0.558946 | + | 0.149769i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.8564 | + | 24.0000i | 0.467099 | + | 0.809040i | ||||
\(881\) | 24.2487i | 0.816960i | 0.912767 | + | 0.408480i | \(0.133941\pi\) | ||||
−0.912767 | + | 0.408480i | \(0.866059\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 14.0000i | − | 0.471138i | −0.971858 | − | 0.235569i | \(-0.924305\pi\) | ||
0.971858 | − | 0.235569i | \(-0.0756953\pi\) | |||||||
\(884\) | −46.7654 | + | 27.0000i | −1.57289 | + | 0.908108i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.3468 | + | 42.3468i | 0.381203 | + | 1.42267i | ||||
\(887\) | 38.1051 | 1.27944 | 0.639722 | − | 0.768606i | \(-0.279049\pi\) | ||||
0.639722 | + | 0.768606i | \(0.279049\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | + | 10.3923i | −0.402467 | + | 0.348547i | ||||
\(890\) | −30.0000 | − | 30.0000i | −1.00560 | − | 1.00560i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −27.0000 | + | 15.5885i | −0.904027 | + | 0.521940i | ||||
\(893\) | −3.00000 | −0.100391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.66025 | + | 15.0000i | 0.289480 | + | 0.501395i | ||||
\(896\) | 13.0718 | + | 26.9282i | 0.436698 | + | 0.899608i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.51666 | − | 35.5167i | 0.317575 | − | 1.18521i | ||||
\(899\) | −12.9904 | − | 22.5000i | −0.433253 | − | 0.750417i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.50000 | + | 2.59808i | 0.149917 | + | 0.0865545i | ||||
\(902\) | 4.73205 | − | 1.26795i | 0.157560 | − | 0.0422181i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −51.9090 | − | 13.9090i | −1.72647 | − | 0.462605i | ||||
\(905\) | 60.0000 | 1.99447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.00000i | − | 0.0664089i | −0.999449 | − | 0.0332045i | \(-0.989429\pi\) | ||
0.999449 | − | 0.0332045i | \(-0.0105712\pi\) | |||||||
\(908\) | −12.0000 | − | 6.92820i | −0.398234 | − | 0.229920i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −55.7654 | − | 37.7654i | −1.84860 | − | 1.25191i | ||||
\(911\) | 11.2583 | + | 6.50000i | 0.373005 | + | 0.215355i | 0.674771 | − | 0.738028i | \(-0.264243\pi\) |
−0.301765 | + | 0.953382i | \(0.597576\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00000 | + | 5.19615i | 0.297857 | + | 0.171968i | ||||
\(914\) | −4.09808 | + | 1.09808i | −0.135552 | + | 0.0363211i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.46410 | − | 6.00000i | 0.114457 | − | 0.198246i | ||||
\(917\) | −24.0000 | − | 27.7128i | −0.792550 | − | 0.915158i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.33013 | + | 2.50000i | 0.142838 | + | 0.0824674i | 0.569716 | − | 0.821842i | \(-0.307053\pi\) |
−0.426878 | + | 0.904309i | \(0.640387\pi\) | |||||||
\(920\) | −27.7128 | + | 27.7128i | −0.913664 | + | 0.913664i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −32.9090 | + | 32.9090i | −1.08380 | + | 1.08380i | ||||
\(923\) | 5.19615 | + | 9.00000i | 0.171033 | + | 0.296239i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.5000 | − | 18.1865i | 0.345238 | − | 0.597970i | ||||
\(926\) | 12.0788 | + | 45.0788i | 0.396935 | + | 1.48138i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.32051 | − | 27.3205i | 0.240307 | − | 0.896840i | ||||
\(929\) | 19.5000 | − | 11.2583i | 0.639774 | − | 0.369374i | −0.144753 | − | 0.989468i | \(-0.546239\pi\) |
0.784528 | + | 0.620094i | \(0.212906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.52628 | + | 7.50000i | 0.312211 | + | 0.245803i | ||||
\(932\) | −1.73205 | + | 1.00000i | −0.0567352 | + | 0.0327561i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.73205 | − | 1.73205i | −0.0566744 | − | 0.0566744i | ||||
\(935\) | 31.1769 | − | 18.0000i | 1.01959 | − | 0.588663i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.46410i | 0.113167i | 0.998398 | + | 0.0565836i | \(0.0180208\pi\) | ||||
−0.998398 | + | 0.0565836i | \(0.981979\pi\) | |||||||
\(938\) | 33.5885 | + | 2.41154i | 1.09670 | + | 0.0787397i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0000 | −0.391397 | ||||||||
\(941\) | 22.5000 | + | 12.9904i | 0.733479 | + | 0.423474i | 0.819694 | − | 0.572802i | \(-0.194144\pi\) |
−0.0862145 | + | 0.996277i | \(0.527477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.46410 | + | 6.00000i | 0.112807 | + | 0.195387i | ||||
\(944\) | 6.92820 | 0.225494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.0000 | − | 22.0000i | −0.715282 | − | 0.715282i | ||||
\(947\) | 37.2391 | − | 21.5000i | 1.21011 | − | 0.698656i | 0.247325 | − | 0.968933i | \(-0.420448\pi\) |
0.962783 | + | 0.270276i | \(0.0871151\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.5000 | + | 54.5596i | −1.02253 | + | 1.77108i | ||||
\(950\) | 12.1244 | + | 12.1244i | 0.393366 | + | 0.393366i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 34.9808 | − | 16.9808i | 1.13373 | − | 0.550350i | ||||
\(953\) | −44.0000 | −1.42530 | −0.712650 | − | 0.701520i | \(-0.752505\pi\) | ||||
−0.712650 | + | 0.701520i | \(0.752505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.1244 | + | 21.0000i | 0.392335 | + | 0.679544i | ||||
\(956\) | 22.0000 | 0.711531 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.60770 | + | 28.3923i | −0.245793 | + | 0.917314i | ||||
\(959\) | 13.8564 | + | 16.0000i | 0.447447 | + | 0.516667i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.00000 | + | 3.46410i | 0.0645161 | + | 0.111745i | ||||
\(962\) | 21.2942 | + | 5.70577i | 0.686553 | + | 0.183961i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.46410 | − | 6.00000i | 0.111571 | − | 0.193247i | ||||
\(965\) | 27.0000 | + | 15.5885i | 0.869161 | + | 0.501810i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.3634 | − | 28.5000i | 1.58742 | − | 0.916498i | 0.593691 | − | 0.804693i | \(-0.297670\pi\) |
0.993730 | − | 0.111805i | \(-0.0356633\pi\) | |||||||
\(968\) | −14.0000 | + | 14.0000i | −0.449977 | + | 0.449977i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.00000 | + | 6.00000i | 0.192648 | + | 0.192648i | ||||
\(971\) | −2.59808 | + | 4.50000i | −0.0833762 | + | 0.144412i | −0.904698 | − | 0.426053i | \(-0.859904\pi\) |
0.821322 | + | 0.570465i | \(0.193237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.5000 | − | 56.2917i | 0.625141 | − | 1.80463i | ||||
\(974\) | 8.41858 | + | 31.4186i | 0.269749 | + | 1.00672i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.0000 | + | 10.3923i | 0.576166 | + | 0.332650i | ||||
\(977\) | −23.5000 | + | 40.7032i | −0.751832 | + | 1.30221i | 0.195103 | + | 0.980783i | \(0.437496\pi\) |
−0.946934 | + | 0.321428i | \(0.895837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.66025 | + | 15.0000i | −0.276783 | + | 0.479402i | ||||
\(980\) | 38.1051 | + | 30.0000i | 1.21722 | + | 0.958315i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.95448 | − | 25.9545i | −0.221926 | − | 0.828241i | ||||
\(983\) | −17.3205 | −0.552438 | −0.276219 | − | 0.961095i | \(-0.589082\pi\) | ||||
−0.276219 | + | 0.961095i | \(0.589082\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.6410i | 1.10375i | ||||||||
\(986\) | −35.4904 | − | 9.50962i | −1.13024 | − | 0.302848i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.00000 | + | 15.5885i | −0.286328 | + | 0.495935i | ||||
\(989\) | 22.0000 | − | 38.1051i | 0.699559 | − | 1.21167i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.4352 | + | 24.5000i | −1.34800 | + | 0.778268i | −0.987966 | − | 0.154671i | \(-0.950568\pi\) |
−0.360034 | + | 0.932939i | \(0.617235\pi\) | |||||||
\(992\) | 7.60770 | − | 28.3923i | 0.241545 | − | 0.901457i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.26795 | − | 6.73205i | −0.103653 | − | 0.213528i | ||||
\(995\) | −5.19615 | + | 3.00000i | −0.164729 | + | 0.0951064i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 24.2487i | − | 0.767964i | −0.923340 | − | 0.383982i | \(-0.874552\pi\) | ||
0.923340 | − | 0.383982i | \(-0.125448\pi\) | |||||||
\(998\) | 2.73205 | + | 0.732051i | 0.0864816 | + | 0.0231727i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.2.n.a.19.2 | 4 | ||
3.2 | odd | 2 | 252.2.n.a.187.1 | yes | 4 | ||
4.3 | odd | 2 | inner | 756.2.n.a.19.1 | 4 | ||
7.3 | odd | 6 | 756.2.bj.a.451.2 | 4 | |||
9.4 | even | 3 | 756.2.bj.a.523.2 | 4 | |||
9.5 | odd | 6 | 252.2.bj.a.103.1 | yes | 4 | ||
12.11 | even | 2 | 252.2.n.a.187.2 | yes | 4 | ||
21.17 | even | 6 | 252.2.bj.a.115.1 | yes | 4 | ||
28.3 | even | 6 | 756.2.bj.a.451.1 | 4 | |||
36.23 | even | 6 | 252.2.bj.a.103.2 | yes | 4 | ||
36.31 | odd | 6 | 756.2.bj.a.523.1 | 4 | |||
63.31 | odd | 6 | inner | 756.2.n.a.199.1 | 4 | ||
63.59 | even | 6 | 252.2.n.a.31.2 | yes | 4 | ||
84.59 | odd | 6 | 252.2.bj.a.115.2 | yes | 4 | ||
252.31 | even | 6 | inner | 756.2.n.a.199.2 | 4 | ||
252.59 | odd | 6 | 252.2.n.a.31.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.n.a.31.1 | ✓ | 4 | 252.59 | odd | 6 | ||
252.2.n.a.31.2 | yes | 4 | 63.59 | even | 6 | ||
252.2.n.a.187.1 | yes | 4 | 3.2 | odd | 2 | ||
252.2.n.a.187.2 | yes | 4 | 12.11 | even | 2 | ||
252.2.bj.a.103.1 | yes | 4 | 9.5 | odd | 6 | ||
252.2.bj.a.103.2 | yes | 4 | 36.23 | even | 6 | ||
252.2.bj.a.115.1 | yes | 4 | 21.17 | even | 6 | ||
252.2.bj.a.115.2 | yes | 4 | 84.59 | odd | 6 | ||
756.2.n.a.19.1 | 4 | 4.3 | odd | 2 | inner | ||
756.2.n.a.19.2 | 4 | 1.1 | even | 1 | trivial | ||
756.2.n.a.199.1 | 4 | 63.31 | odd | 6 | inner | ||
756.2.n.a.199.2 | 4 | 252.31 | even | 6 | inner | ||
756.2.bj.a.451.1 | 4 | 28.3 | even | 6 | |||
756.2.bj.a.451.2 | 4 | 7.3 | odd | 6 | |||
756.2.bj.a.523.1 | 4 | 36.31 | odd | 6 | |||
756.2.bj.a.523.2 | 4 | 9.4 | even | 3 |